Problem: Tiffany is 5 times as old as Gabriela. Eight years ago, Tiffany was 9 times as old as Gabriela. How old is Tiffany now?
Answer: We can use the given information to write down two equations that describe the ages of Tiffany and Gabriela. Let Tiffany's current age be $t$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $t = 5g$ Eight years ago, Tiffany was $t - 8$ years old, and Gabriela was $g - 8$ years old. The information in the second sentence can be expressed in the following equation: $t - 8 = 9(g - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $t$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = t / 5$ . Substituting this into our second equation, we get: $t - 8 = 9($ $(t / 5)$ $- 8)$ which combines the information about $t$ from both of our original equations. Simplifying the right side of this equation, we get: $t - 8 = \dfrac{9}{5} t - 72$ Solving for $t$ , we get: $\dfrac{4}{5} t = 64$ $t = \dfrac{5}{4} \cdot 64 = 80$.